Visually displaying multipliers

As I'm preparing a blog about another real-world study of Covid-19 vaccines, I came across the following chart (the chart title is mine).

React1_original

As background, this is the trend in Covid-19 cases in the U.K. in the last couple of months, courtesy of OurWorldinData.org.

Junkcharts_owid_uk_case_trend_july_august_2021

The React-1 Study sends swab kits to randomly selected people in England in order to assess the prevalence of Covid-19. Every month, there is a new round of returned swabs that are tested for Covid-19. This measurement method captures asymptomatic cases although it probably missed severe and hospitalized cases. Despite having some shortcomings, this is a far better way to measure cases than the hotch-potch assembling of variable-quality data submitted by different jurisdictions that has become the dominant source of our data.

Rounds 12 and 13 captured an inflection point in the pandemic in England. The period marked the beginning of the end of the belief that widespread vaccination will end the pandemic.

The chart I excerpted up top broke the data down by age groups. The column heights represent the estimated prevalence of Covid-19 during each round - also, described precisely in the paper as "swab positivity." Based on the study's design, one may generalize the prevalence to the population at large. About 1.5% of those aged 13-24 in England are estimated to have Covid-19 around the time of Round 13 (roughly early July).

The researchers came to the following conclusion:

We show that the third wave of infections in England was being driven primarily by the Delta variant in younger, unvaccinated people. This focus of infection offers considerable scope for interventions to reduce transmission among younger people, with knock-on benefits across the entire population... In our data, the highest prevalence of infection was among 12 to 24 year olds, raising the prospect that vaccinating more of this group by extending the UK programme to those aged 12 to 17 years could substantially reduce transmission potential in the autumn when levels of social mixing increase

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Raise your hand if the graphics software you prefer dictates at least one default behavior you can't stand. I'm sure most hands are up in the air. No matter how much you love the software, there is always something the developer likes that you don't.

The first thing I did with today's chart is to get rid of all such default details.

Redo_react1_cleanup

For me, the bottom chart is cleaner and more inviting.

***

The researchers wanted readers to think in terms of Round 3 numbers as multiples of Round 2 numbers. In the text, they use statements such as:

weighted prevalence in round 13 was nine-fold higher in 13-17 year olds at 1.56% (1.25%, 1.95%) compared with 0.16% (0.08%, 0.31%) in round 12

It's not easy to perceive a nine-fold jump from the paired column chart, even though this chart form is better than several others. I added some subtle divisions inside each orange column in order to facilitate this task:

Redo_react1_multiples

I have recommended this before. I'm co-opting pictograms in constructing the column chart.

An alternative is to plot everything on an index scale although one would have to drop the prevalence numbers.

***

The chart requires an additional piece of context to interpret properly. I added each age group's share of the population below the chart - just to illustrate this point, not to recommend it as a best practice.

Redo_react1_multiples_popshare

The researchers concluded that their data supported vaccinating 13-17 year olds because that group experienced the highest multiplier from Round 12 to Round 13. Notice that the 13-17 year old age group represents only 6 percent of England's population, and is the least populous age group shown on the chart.

The neighboring 18-24 age group experienced a 4.5 times jump in prevalence in Round 13 so this age group is doing much better than 13-17 year olds, right? Not really.

While the same infection rate was found in both age groups during this period, the slightly older age group accounted for 50% more cases -- and that's due to the larger share of population.

A similar calculation shows that while the infection rate of people under 24 is about 3 times higher than that of those 25 and over, both age groups suffered over 175,000 infections during the Round 3 time period (the difference between groups was < 4,000).  So I don't agree that focusing on 13-17 year olds gives England the biggest bang for the buck: while they are the most likely to get infected, their cases account for only 14% of all infections. Almost half of the infections are in people 25 and over.

 


Check your presumptions while you're reading this chart about Israel's vaccination campaign

On July 30, Israel began administering third doses of mRNA vaccines to targeted groups of people. This decision was controversial since there is no science to support it. The policymakers do have educated guesses by experts based on best-available information. By science, I mean actual evidence. Since no one has previously been given three shots, there can be no data on which anyone can root such a decision. Nevertheless, the pandemic does not always give us time to collect relevant data, and so speculative analysis has found its calling.

Dvir Aran, at Technion, has been diligently tracking the situation in Israel on his Twitter. Ten days after July 30, he posted the following chart, which immediately led many commentators to bounce out of their seats crowning the third shot as a magic bullet. Notably, Dvir himself did not endorse such a claim. (See here to learn how other hasty conclusions by experts have fared.)

When you look at Dvir's chart, what do we see?

Dvir_aran_chart

Possibly one of the following two things, depending on what concern you have in your head.

1) The red line sits far above the other two lines, showing that unvaccinated people are much more likely to get infected.

2) The blue line diverges from the green line almost immediately after the 3rd shots started getting into arms, showing that the 3rd shot is super effective.

If you take another moment to look, you might start asking questions, as many in Twitter world did. Dvir was startlingly efficient at answering these queries.

A) Does the green line represent people with 2 or 3 doses, or is it strictly 2 doses? Aron asked this question and got the answer (the former):

AronBrand_israelcases_twoorthreedoses

It's time to check our presumptions. When you read that chart, did you presume it's exactly 2 doses or did you presume it's 2 or 3 doses? Or did you immediately spot the ambiguity? As I said in this article, graphs attain efficiency at communication because the designer leverages unspoken rules - the chart conveys certain information without explicitly placing it on the chart. But this can backfire. In this case, I presumed the three lines to display three non-overlapping groups of people, and thus the green line indicates those with 2 doses but not 3. That presumption led me to misinterpret what's on the chart.

B) What is the denominator of the case rates? Is it literal - by that I mean, all unvaccinated people for the red line, and all people with 3 doses for the blue line? Or is the denominator the population of Israel, the same number for all three lines? Lukas asked this question, and got the answer (the former).

Lukas_denominator

C) Since third shots are recommended for 60 year olds and over who were vaccinated at least 5 months ago, and most unvaccinated Israelis are below 60, this answer opens the possibility that the lines compare apples and oranges. Joe. S. asked about this, and received an answer (all lines display only 60 year olds and over.)

Joescholar_basepopulationquestion

Jason P. asked, and learned that the 5-month-out criterion is immaterial since 90% of the vaccinated have already reached that time point.

JasonPogue_5monthsout

D) We have even more presumptions. Like me, did you presume that the red line represents the "unvaccinated," meaning people who have not had any vaccine shots? If so, we may both be wrong about this. It has become the norm by vaccine researchers to lump "partially vaccinated" people with "unvaccinated", and call this combined group "unvaccinated". Here is an excerpt from a recent report from Public Health Ontario (link to PDF), which clearly states this unintuitive counting rule:

Ontario_case_definition

Notice that in this definition, someone who got infected within 14 days of the first shot is classified as an "unvaccinated" case and not a "partially vaccinated case".

In the following tweet, Dvir gave a hint of what he plotted:

Dvir_group_definition

In a previous analysis, he averaged the rates of people with 0 doses and 1 dose, which is equivalent to combining them and calling them unvaccinated. It's unclear to me what he did to the 1-dose subgroup in our featured chart - did it just vanish from the chart? (How people and cases are classified into these groups is a major factor in all vaccine effectiveness calculations - a topic I covered here. Unfortunately, most published reports do a poor job explaining what the analysts did).

E) Did you presume that all three lines are equally important? That's far from true. Since Israel is the world champion in vaccination, the bulk of the 60+ population form the green line. I asked Dvir and he responded that only 7.5%, or roughly 100K are unvaccinated.

DvirAran_proportionofunvaccinated

That means 1.2 million people are part of the green line, 12 times higher. There are roughly 50 cases per day among unvaccinated, and 370 daily cases among those with 2 or 3 doses. In other words, vaccinated people account for almost 90% of all cases.

Yes, this is inevitable when over 90% of the age group have been vaccinated (but it is predictable on the first day someone blasted everywhere that real-world VE is proved by the fact that almost all new cases were in the unvaccinated.)

If your job is to minimize infections, you should be spending most of your time thinking about the 370 cases among vaccinated than the 50 cases among unvaccinated. If you halve the case rate, that would be a difference of 185 cases vs 25. In Israel, the vaccination campaign has already succeeded; it's time to look forward, which is exactly why they are re-focusing on the already vaccinated.

***

If what you worry about most is the effectiveness of the original two-dose regimen, Dvir's chart raises a puzzle. Ignore the blue line, and remember that the green line already includes everybody represented by the blue line.

In the following chart, I removed the blue line, and added reference lines in dashed purple that correspond to 25%, 50% and 75% vaccine effectiveness. The data plotted on this chart are unadjusted case rates. A 75% effective vaccine cuts case rate by three quarters.

Junkcharts_dviraran_israel_threeshotschart

This chart shows the 2-dose mRNA vaccine was nowhere near 90% effective. (As regular readers know, I don't endorse this simplistic calculation and have outlined the problems here, but this style of calculation keeps getting published and passed around. Those who use it to claim real-world studies confirm prior clinical trial outcomes can either (a) insist on using it and retract their earlier conclusions, or (b) admit that such a calculation was, and is, a bad take.)

Also observe how the vaccinated (green) line is moving away from the unvaccinated (red) line. The vaccine apparently is becoming more effective, which runs counter to the trend used by the Israeli government to justify third doses. This improvement also precedes the start of the third-shot campaign. When the analytical method is bad, it generates all sorts of spurious findings.

***

As Dvir said, it is premature to comment on the third doses based on 10 days of data. For one thing, the vaccine developers insist that their vaccines must be given 14 days to work. In a typical calculation, all of the cases in the blue line fall outside the case-counting window. The effective number of cases that would be attributed to the 3-dose group right now is zero, and the vaccine effectiveness using the standard methodology is 100%, even better than shown in the chart.

There is an alternative interpretation of this graph. Statisticians call this the selection effect. On July 30, the blue line split out of the green: some people were selected to receive the 3rd dose - this includes an official selection (the government makes certain subgroups eligible) as well as a self-selection (within the eligible subgroup, certain people decide to get the 3rd shot earlier.) If those who are less exposed to the virus, or more risk averse, get the shots first, then all that is happening may be that we have split off a high VE subgroup from the green line. Even if the third shot were useless, the selection effect itself could explain the gap.

Statistics is about grays. It's not either-or. It's usually some of each. If you feel like Groundhog Day, you're getting the picture. When they rolled out two doses, we lived through an optimistic period in which most experts rejoiced about 90-100% real-world effectiveness, and then as more people get vaccinated, the effect washed away. The selection effect gradually disappears when vaccination becomes widespread. Are we starting a new cycle of hope and despair? We'll find out soon enough.


What metaphors give, they take away

Aleks pointed me to the following graphic making the rounds on Twitter:

Whyaxis_covid_men

It's being passed around as an example of great dataviz.

The entire attraction rests on a risque metaphor. The designer is illustrating a claim that Covid-19 causes erectile dysfunction in men.

That's a well-formed question so in using the Trifecta Checkup, that's a pass on the Q corner.

What about the visual metaphor? I advise people to think twice before using metaphors because these devices can give as they can take. This example is no exception. Some readers may pay attention to the orientation but other readers may focus on the size.

I pulled out the tape measure. Here's what I found.

Junkcharts_covid_eds

The angle is accurate on the first chart but the diameter has been exaggerated relative to the other. The angle is slightly magnified in the bottom chart which has a smaller circumference.

***

Let's look at the Data to round out our analysis. They come from a study from Italy (link), utilizing survey responses. There were 25 male respondents in the survey who self-reported having had Covid-19. Seven of these submitted answers to a set of five questions that were "suggestive of erectile dysfunction". (This isn't as arbitrary as it sounds - apparently it is an internationally accepted way of conducting reseach.) Seven out of 25 is 28 percent. Because the sample size is small, the 95% confidence range is 10% to 46%.

The researchers then used the propensity scoring method to find 3 matches per each infected person. Each match is a survey respondent who did not self-report having had Covid-19. See this post about a real-world vaccine study to learn more about propensity scoring. Among the 75 non-infected men, 7 were judged to have ED. The 95% range is 3% to 16%.

The difference between the two subgroups is quite large. The paper also includes other research that investigates the mechanisms that can explain the observed correlation. Nevertheless, the two proportions depicted in the chart have wide error bars around them.

I have always had a question about analysis using this type of survey data (including my own work). How do they know that ED follows infection rather than precedes it? One of the inviolable rules of causation is that the effect follows the cause. If it's a series of surveys, the sequencing may be measurable but a single survey presents challenges. 

The headline of the dataviz is "Get your vaccines". This comes from a "story time" moment in the paper. On page 1, under Discussion and conclusion, they inserted the sentence "Universal vaccination against COVID-19 and the personal protective equipment could possibly have the added benefit of preventing sexual dysfunctions." Nothing in the research actually supports this claim. The only time the word "vaccine" appears in the entire paper is on that first page.

"Story time" is the moment in a scientific paper when the researchers - after lulling readers to sleep over some interesting data - roll out statements that are not supported by the data presented before.

***

The graph succeeds in catching people's attention. The visual metaphor works in one sense but not in a different sense.

 

P.S. [8/6/2021] One final note for those who do care about the science: the internet survey not surprisingly has a youth bias. The median age of 25 infected people was 39, maxing out at 45 while the median of the 75 not infected was 42, maxing out at 49.


Vaccine researchers discard the start-at-zero rule

I struggled to decide on which blog to put this post. The reality is it bridges the graphical and analytical sides of me. But I ultimately placed it on the dataviz blog because that's where today's story starts.

Data visualization has few set-in-stone rules. If pressed for one, I'd likely cite the "start-at-zero" rule, which has featured regularly on Junk Charts (here, here, and here, for example). This rule only applies to a bar chart, where the heights (and thus, areas) of the bars should encode the data.

Here is a stacked column chart that earns boos from us:

Kfung_stackedcolumn_notstartingatzero_0

I made it so I'm downvoting myself. What's wrong with this chart? The vertical axis starts at 42 instead of zero. I've cropped out exactly 42 units from each column. Therefore, the column areas are no longer proportional to the ratio of the data. Forty-two is 84% of the column A while it is 19% of column B. By shifting the x-axis, I've made column B dwarf column A. For comparison, I added a second chart that has the x-axis start at zero.

Kfung_stackedcolumn_notstartatzero

On the right side, Column B is 22 times the height of column A. On the left side, it is 4 times as high. Both are really the same chart, except one has its legs chopped off.

***

Now, let me reveal the data behind the above chart. It is a re-imagination of the famous cumulative case curve from the Pfizer vaccine trial.

Pfizerfda_figure2_cumincidencecurves

I transferred the data to a stacked column chart. Each column block shows the incremental cases observed in a given week of the trial. All the blocks stacked together rise to the total number of cases observed by the time the interim analysis was presented to the FDA.

Observe that in the cumulative cases chart, the count starts at zero on Day 0 (first dose). This means the chart corresponds to the good stacked column chart, with the x-axis starting from zero on Day 0.

Kfung_pfizercumcases_stackedcolumn

The Pfizer chart above is, however, disconnected from the oft-chanted 95% vaccine efficacy number. You can't find this number on there. Yes, everyone has been lying to you. In a previous post, I did the math, and if you trace the vaccine efficacy throughout the trial, you end up at about 80% toward the right, not 95%.

Pfizer_cumcases_ve_vsc_published

How can they conclude VE is 95% but show a chart that never reaches that level? The chart was created for a "secondary" analysis included in the report for completeness. The FDA and researchers have long ago decided, before the trials started enrolling people, that they don't care about the cumulative case curve starting on Day 0. The "primary" analysis counts cases starting 7 days after the second shot, which means Day 29.

The first week that concerns the FDA is Days 29-35 (for Pfizer's vaccine). The vaccine arm saw 41 cases in the first 28 days of the trial. In effect, the experts chop the knees off the column chart. When they talk about 95% VE, they are looking at the column chart with the axis starting at 42.

Kfung_pfizercumcases_stackedcolumn_chopped

Yes, that deserves a boo.

***

It's actually even worse than that, if you could believe it.

The most commonly cited excuse for the knee-chop is that any vaccine is expected to be useless in the first X days (X being determined after the trial ends when they analyze the data). A recently published "real world" analysis of the situation in Israel contains a lengthy defense of this tactic, in which they state:

Strictly speaking, the vaccine effectiveness based on this risk ratio overestimates the overall vaccine effectiveness in our study because it does not include the early follow-up period during which the vaccine has no detectable effect (and thus during which the ratio is 1). [Appendix, Supplement 4]

Assuming VE = 0 prior to day X is equivalent to stipulating that the number of cases found in the vaccine arm is the same (within margin of error) as the number of cases in the placebo arm during the first X days.

That assumption is refuted by the Pfizer trial (and every other trial that has results so far.)

The Pfizer/Biontech vaccine was not useless during the first week. It's not 95% efficacious, more like 16%. In the second week, it improves to 33%, and so on. (See the VE curve I plotted above for the Pfizer trial.)

What happened was all the weeks before which the VE has not plateaued were dropped.

***

So I was simplifying the picture by chopping same-size blocks from both columns in the stacked column chart. Contrary to the no-effect assumption, the blocks at the bottom of each column are of different sizes. Much more was chopped from the placebo arm than from the vaccine arm.

You'd think that would unjustifiably favor the placebo. Not true! As almost all the cases on the vaccine arm were removed, the remaining cases on the placebo arm are now many multiples of those on the vaccine arm.

The following shows what the VE would have been reported if they had started counting cases from day X. The first chart counts all cases from first shot. The second chart removes the first two weeks of cases, corresponding to the analysis that other pharmas have done, namely, evaluate efficacy from 14 days after the first dose. The third chart removes even more cases, and represents what happens if the analysis is conducted from second dose. The fourth chart is the official Pfizer analysis, which began days after the second shot. Finally, the fifth chart shows analysis begining from 14 days after the second shot, the window selected by Moderna and Astrazeneca.

Kfung_howvaccinetrialsanalyzethedata

The premise that any vaccine is completely useless for a period after administration is refuted by the actual data. By starting analysis windows at some arbitrary time, the researchers make it unnecessarily difficult to compare trials. Selecting the time of analysis based on the results of a single trial is the kind of post-hoc analysis that statisticians have long warned leads to over-estimation. It's equivalent to making the vertical axis of a column chart start above zero in order to exaggerate the relative heights of the columns.

 

P.S. [3/1/2021] See comment below. I'm not suggesting vaccines are useless. They are still a miracle of science. I believe the desire to report a 90% VE number is counterproductive. I don't understand why a 70% or 80% effective vaccine is shameful. I really don't.


Illustrating differential growth rates

Reader Mirko was concerned about a video published in Germany that shows why the new coronavirus variant is dangerous. He helpfully provided a summary of the transcript:

The South African and the British mutations of the SARS-COV-2 virus are spreading faster than the original virus. On average, one infected person infects more people than before. Researchers believe the new variant is 50 to 70 % more transmissible.

Here are two key moments in the video:

Germanvid_newvariant1

This seems to be saying the original virus (left side) replicates 3 times inside the infected person while the new variant (right side) replicates 19 times. So we have a roughly 6-fold jump in viral replication.

Germanvid_newvariant2

Later in the video, it appears that every replicate of the old virus finds a new victim while the 19 replicates of the new variant land on 13 new people, meaning 6 replicates didn't find a host.

As Mirko pointed out, the visual appears to have run away from the data. (In our Trifecta Checkup, we have a problem with the arrow between the D and the V corners. What the visual is saying is not aligned with what the data are saying.)

***

It turns out that the scientists have been very confusing when talking about the infectiousness of this new variant. The most quoted line is that the British variant is "50 to 70 percent more transmissible". At first, I thought this is a comment on the famous "R number". Since the R number around December was roughly 1 in the U.K, the new variant might bring the R number up to 1.7.

However, that is not the case. From this article, it appears that being 5o to 70 percent more transmissible means R goes up from 1 to 1.4. R is interpreted as the average number of people infected by one infected person.

Mirko wonders if there is a better way to illustrate this. I'm sure there are many better ways. Here's one I whipped up:

Junkcharts_redo_germanvideo_newvariant

The left side is for the 40% higher R number. Both sides start at the center with 10 infected people. At each time step, if R=1 (right side), each of the 10 people infects 10 others, so the total infections increase by 10 per time step. It's immediately obvious that a 40% higher R is very serious indeed. Starting with 10 infected people, in 10 steps, the total number of infections is almost 1,000, almost 10 times higher than when R is 1.

The lines of the graphs simulate the transmission chains. These are "average" transmission chains since R is an average number.

 

P.S. [1/29/2021: Added the missing link to the article in which it is reported that 50-70 percent more transmissible implies R increasing by 40%.]

 

 


Reading an infographic about our climate crisis

Let's explore an infographic by SCMP, which draws attention to the alarming temperature recorded at Verkhoyansk in Russia on June 20, 2020. The original work was on the back page of the printed newspaper, referred to in this tweet.

This view of the globe brings out the two key pieces of evidence presented in the infographic: the rise in temperature in unexpected places, and the shrinkage of the Arctic ice.

Scmp_russianheat_1a

A notable design decision is to omit the color scale. On inspection, the scale is present - it was sewn into the graphic.

Scmp_russianheat_colorscale

I applaud this decision as it does not take the reader's eyes away from the graphic. Some information is lost as the scale isn't presented in full details but I doubt many readers need those details.

A key takeaway is that the temperature in Verkhoyansk, which is on the edge of the Arctic Circle, was the same as in New Delhi in India on that day. We can see how the red was encroaching upon the Arctic Circle.

***Scmp_russianheat_2a

Next, the rapid shrinkage of the Arctic ice is presented in two ways. First, a series of maps.

The annotations are pared to the minimum. The presentation is simple enough such that we can visually judge that the amount of ice cover has roughly halved from 1980 to 2009.

A numerical measure of the drop is provided on the side.

Then, a line chart reinforces this message.

The line chart emphasizes change over time while the series of maps reveals change over space.

Scmp_russianheat_3a

This chart suggests that the year 2020 may break the record for the smallest ice cover since 1980. The maps of Australia and India provide context to interpret the size of the Arctic ice cover.

I'd suggest reversing the pink and black colors so as to refer back to the blue and pink lines in the globe above.

***

The final chart shows the average temperature worldwide and in the Arctic, relative to a reference period (1981-2000).

Scmp_russianheat_4

This one is tough. It looks like an area chart but it should be read as a line chart. The darker line is the anomaly of Arctic average temperature while the lighter line is the anomaly of the global average temperature. The two series are synced except for a brief period around 1940. Since 2000, the temperatures have been dramatically rising above that of the reference period.

If this is a stacked area chart, then we'd interpret the two data series as summable, with the sum of the data series signifying something interesting. For example, the market shares of different web browsers sum to the total size of the market.

But the chart above should not be read as a stacked area chart because the outside envelope isn't the sum of the two anomalies. The problem is revealed if we try to articulate what the color shades mean.

Scmp_russianheat_4_inset

On the far right, it seems like the dark shade is paired with the lighter line and represents global positive anomalies while the lighter shade shows Arctic's anomalies in excess of global. This interpretation only works if the Arctic line always sits above the global line. This pattern is broken in the late 1990s.

Around 1999, the Arctic's anomaly is negative while the global anomaly is positive. Here, the global anomaly gets the lighter shade while the Arctic one is blue.

One possible fix is to encode the size of the anomaly into the color of the line. The further away from zero, the darker the red/blue color.

 

 


A beautiful curve and its deadly misinterpretation

When the preliminary analyses of their Phase 3 trials came out , vaccine developers pleased their audience of scientists with the following data graphic:

Pfizerfda_cumcases

The above was lifted out of the FDA briefing document for the Pfizer / Biontech vaccine.

Some commentators have honed in on the blue line for the vaccinated arm of the Pfizer trial.

Junkcharts_pfizerfda_redo_vaccinecases

Since the vertical axis shows cumulative number of cases, it is noted that the vaccine reached peak efficacy after 14 days following the first dose. The second dose was administered around Day 21. At this point, the vaccine curve appeared almost flat. Thus, these commentators argued, we should make a big bet on the first dose.

***

The chart is indeed very beautiful. It's rare to see such a huge gap between the test group and the control group. Notice that I just described the gap between test and control. That's what a statistician is looking at in that chart - not the blue line, but the gap between the red and blue lines.

Imagine: if the curve for the placebo group looked the same as that for the vaccinated group, then the chart would lose all its luster. Screams of victory would be replaced by tears of sadness.

Here I bring back both lines, and you should focus on the gaps between the lines:

Junkcharts_pfizerfda_redo_twocumcases

Does the action stop around day 14? The answer is a resounding No! In fact, the red line keeps rising so over time, the vaccine's efficacy improves (since VE is a ratio between the two groups).

The following shows the vaccine efficacy curve:

Junkcharts_pfizerfda_redo_ve

Right before the second dose, VE is just below 50%. VE keeps rising and reaches 70% by day 50, which is about a month after the second dose.

If the FDA briefing document has shown the VE curve, instead of the cumulative-cases curve, few would argue that you don't need the second dose!

***

What went wrong here? How come the beautiful chart may turn out to be lethal? (See this post on my book blog for reasons why I think foregoing or delaying the second dose will exacerbate the pandemic.)

It's a bit of bait and switch. The original chart plots cumulative case counts, separately for each treatment group. Cumulative case counts are inputs to computing vaccine efficacy. It is true that as the blue line for the vaccine flattens, VE would likely rise. But the case count for the vaccine group is an imperfect proxy for VE. As I showed above, the VE continues to gain strength long after the vaccine case count has levelled.

The important lesson for data visualization designers is: plot the metric that matters to decision-makers; avoid imperfect proxies.

 

P.S. [1/19/2021: For those who wants to get behind the math of all this, the following several posts on my book blog will help.

One-dose Pfizer is not happening, and here's why

The case for one-dose vaccines is lacking key details

One-dose vaccine strategy elevates PR over science

]

[1/21/2021: The Guardian chimes in with "Single Covid vaccine dose in Israel 'less effective than we thought'" (link). "In remarks reported by Army Radio, Nachman Ash said a single dose appeared “less effective than we had thought”, and also lower than Pfizer had suggested." To their credit, Pfizer has never publicly recommended a one-dose treatment.]

[1/21/2021: For people in marketing or business, I wrote up a new post that expresses the one-dose vs two-dose problem in terms of optimizing an email drip campaign. It boils down to: do you accept that argument that you should get rid of your latter touches because the first email did all the work? Or do you want to run an experiment with just one email before you decide? You can read this on the book blog here.]


Convincing charts showing containment measures work

The disorganized nature of U.S.'s response to the coronavirus pandemic has created a sort of natural experiment that allows data journalists to explore important scientific questions, such as the impact of containment measures on cases and hospitalizations. This New York Times article represents the best of such work.

The key finding of the analysis is beautifully captured by this set of scatter plots:

Policies_cases_hosp_static

Each dot is a state. The cases (left plot) and hospitalizations (right plot) are plotted against the severity of containment measures for November. The negative correlation is unmistakable: the more containment measures taken, the lower the counts.

There are a few features worth noting.

The severity index came from a group at Oxford, and is a number between 0 and 100. The journalists decided to leave out the numerical labels, instead simply showing More and Fewer. This significantly reduces processing time. Readers won't be able to understand the index values anyway without reading the manual.

The index values are doubly encoded. They are first encoded by the location on the horizontal axis and redundantly encoded on the blue-red scale. Ordinarily, I do not like redundant encoding because the reader might assume a third dimension exists. In this case, I had no trouble with it.

The easiest way to see the effect is to ignore the muddy middle and focus on the two ends of the severity index. Those states with the fewest measures - South Dakota, North Dakota, Iowa - are the worst in cases and hospitalizations while those states with the most measures - New York, Hawaii - are among the best. This comparison is similar to what is frequently done in scientific studies, e.g. when they say coffee is good for you, they typically compare heavy drinkers (4 or more cups a day) with non-drinkers, ignoring the moderate and light drinkers.

Notably, there is quite a bit of variability for any level of containment measures - roughly 50 cases per 100,000, and 25 hospitalizations per 100,000. This indicates that containment measures are not sufficient to explain the counts. For example, the hospitalization statistic is affected by the stock of hospital beds, which I assume differ by state.

Whenever we use a scatter plot, we run the risk of xyopia. This chart form invites readers to explain an outcome (y-axis values) using one explanatory variable (on x-axis). There is an assumption that all other variables are unimportant, which is usually false.

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Because of the variability, the horizontal scale has meaningless precision. The next chart cures this by grouping the states into three categories: low, medium and high level of measures.

Cases_over_time_grouped_by_policies

This set of charts extends the time window back to March 1. For the designer, this creates a tricky problem - because states adapt their policies over time. As indicated in the subtitle, the grouping is based on the average severity index since March, rather than just November, as in the scatter plots above.

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The interplay between policy and health indicators is captured by connected scatter plots, of which the Times article included a few examples. Here is what happened in New York:

NewYork_policies_vs_cases

Up until April, the policies were catching up with the cases. The policies tightened even after the case-per-capita started falling. Then, policies eased a little, and cases started to spike again.

The Note tells us that the containment severity index is time shifted to reflect a two-week lag in effect. So, the case count on May 1 is not paired with the containment severity index of May 1 but of April 15.

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You can find the full article here.

 

 

 


Podcast highlights

Recently, I made a podcast for Ryan Ray, which you can access here. The link sends you to a 14-day free trial to his newsletter, which is where he publishes his podcasts.

Kaiserfung_warroommedia

Ryan contacted me after he read my book Numbers Rule Your World (link). I was happy to learn that he enjoyed the stories, and during the podcast, he gave an example of how he applied the statistical concepts to other situations.

During the podcast, you will hear:

  • I have a line in my course syllabus that reads "after you take this class, you will not be able to look at numbers (in the media) with a straight face ever again." That's a goal of mine. And it also applies to my books.

  • Why are most statisticians skeptics

  • Figuring out the statistical conclusions is the easy part while the hardest challenge is to find a way to communicate them to a non-technical audience. I went through many drafts before I landed on the precise language used in those stories.

  • Why "correlation is not causation" is not useful practical advice
  • You can't unsee something you've already seen, and this creates hindsight bias
  • The biggest bang for the buck when improving statistical models is improving data quality

  • Some models, such as polls and election forecasts, can be thought of as thermometers measuring the mood of the respondents at the time of polling.

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To hear the podcast, visit Ryan Ray's website.


Deaths as percent neither of cases nor of population. Deaths as percent of normal.

Yesterday, I posted a note about excess deaths on the book blog (link). The post was inspired by a nice data visualization by the New York Times (link). This is a great example of data journalism.

Nyt_excessdeaths_south

Excess deaths is a superior metric for measuring the effect of Covid-19 on public health. It's better than deaths as percent of cases. Also better than percent of the population.What excess deaths measure is deaths as a percent of normal. Normal is usually defined as the average deaths in the respective week in years past.

The red areas indicate how far the deaths in the Southern states are above normal. The highest peak, registered in Texas in late July, is 60 percent above the normal level.

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The best way to appreciate the effort that went into this graphic is to imagine receiving the outputs from the model that computes excess deaths. A three-column spreadsheet with columns "state", "week number" and "estimated excess deaths".

The first issue is unequal population sizes. More populous states of course have higher death tolls. Transforming death tolls to an index pegged to the normal level solves this problem. To produce this index, we divide actual deaths by the normal level of deaths. So the spreadsheet must be augmented by two additional columns, showing the historical average deaths and actual deaths for each state for each week. Then, the excess death index can be computed.

The journalist builds a story around the migration of the coronavirus between different regions as it rages across different states  during different weeks. To this end, the designer first divides the dataset into four regions (South, West, Midwest and Northeast). Within each region, the states must be ordered. For each state, the week of peak excess deaths is identified, and the peak index is used to sort the states.

The graphic utilizes a small-multiples framework. Time occupies the horizontal axis, by convention. The vertical axis is compressed so that the states are not too distant. For the same reason, the component graphs are allowed to overlap vertically. The benefit of the tight arrangement is clearer for the Northeast as those peaks are particularly tall. The space-saving appearance reminds me of sparklines, championed by Ed Tufte.

There is one small tricky problem. In most of June, Texas suffered at least 50 percent more deaths than normal. The severity of this excess death toll is shortchanged by the low vertical height of each component graph. What forced such congestion is probably the data from the Northeast. For example, New York City:

Nyt_excessdeaths_northeast3

 

New York City's death toll was almost 8 times the normal level at the start of the epidemic in the U.S. If the same vertical scale is maintained across the four regions, then the Northeastern states dwarf all else.

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One key takeaway from the graphic for the Southern states is the persistence of the red areas. In each state, for almost every week of the entire pandemic period, actual deaths have exceeded the normal level. This is strong indication that the coronavirus is not under control.

In fact, I'd like to see a second set of plots showing the cumulative excess deaths since March. The weekly graphic is better for identifying the ebb and flow while the cumulative graphic takes measure of the total impact of Covid-19.

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The above description leaves out a huge chunk of work related to computing excess deaths. I assumed the designer receives these estimates from a data scientist. See the related post in which I explain how excess deaths are estimated from statistical models.